Razonamiento configural y organización discursiva en procesos de prueba en contexto geométrico

Resum

In this study, we analyze the status change of the different mathematical affirmations that compose the discursive process in solving proof problems into geometry context. In particular, we focus on the way in which it is developed and organized the written discourse (answer) which allows communicating the solution, with the aim of identifying relationships with the configural reasoning outcomes. For this, we analyze the answers of students in the four grade of compulsory secondary education to four proof problems in a geometrical context. The results highlight the necessity of a change into the status of the mathematical affirmations involved in the reasoning leading to the solution, as well as the development of an argumentation that it should be developed from the accumulation mode to the substitution one. However, the presence of these characteristics of the proof process don’t guarantee that the configural reasoning “truncation” that generates the formal proof will occur, due to, among other factors, the influence exerted by the relevant subconfiguration identified in the reasoning process.